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szcf-weiya committed Dec 23, 2020
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Expand Up @@ -44,12 +44,12 @@ $$

$$
\begin{align}
\Pr(\cal M_m\mid Z)&\propto \Pr(\cal M_m)\cdot\Pr(\mathbf Z\mid \cal M_m)\notag\\
&\propto \Pr(\cal M_m)\cdot \int Pr(\mathbf Z_m\mid \theta_m,\cal M_m)Pr(\theta_m\mid \cal M_m)d\theta_m\tag{8.55}\label{8.55}
\Pr(\cM_m\mid \Z)&\propto \Pr(\cM_m)\cdot\Pr(\Z\mid \cM_m)\notag\\
&\propto \Pr(\M_m)\cdot \int \Pr(\Z \mid \theta_m,\cM_m)\Pr(\theta_m\mid \cM_m)d\theta_m\tag{8.55}\label{8.55}
\end{align}
$$

原则上,可以确定先验 $\Pr(\theta_m\mid \cal M_m)$,然后根据式 \eqref{8.55} 数值上计算后验概率,从而作为模型平均的权重.然而,相比更简单的 BIC 近似,我们没有看到任何实际的证据来表明值得这样做.
原则上,可以确定先验 $\Pr(\theta_m\mid \cM_m)$,然后根据式 \eqref{8.55} 数值上计算后验概率,从而作为模型平均的权重.然而,相比更简单的 BIC 近似,我们没有看到任何实际的证据来表明值得这样做.

我们怎么从频率的角度来实现模型平均?给定平方损失下的预测值 $\hat f_1(x),\hat f_2(x),\ldots, \hat f_M(x)$,我们可以寻找权重 $w=(w_1,w_2,\ldots,w_M)$ 使得

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